### HS AP Calculus

 AP Calculus AB Exam DateONLINE TEST DATE: May, 2020SyllabusAllowed CalculatorsUpdated 2019 AP Calculus AB Framework and Exam DescriptionAll assignments will be posted in VERGE daily until we return to school. If you need to talk to me, email me at bolanle_salaam@dekalbschoolsga.org or contact me through VERGE.Week 1 (Unit 1: Limits)What is Calculus?2.1 Average Rates of Change2.1 Numerical Limit2.2 Definition of a Limit2.2 One Sided Limits vs. Two Sided Limits2.2 Graphical Limits2.3 Limit Rules2.3 Limits Laws2.3 Limits of Polynomials and Rational Functions pg. 97Techniques of Finding LimitsDirect SubstitutionCancellation (Factoring)Radical ConjugateAlgebraic ManipulationMaking use of the formal definition of an absolute valueSpecial Limit: lim as x-> 0 sin(x)/x = 1Week 2 (Unit 1: Limits)2.3 Squeeze Theorem pg. 1012.2 Infinite Limits (Sign Analysis/Limit Analysis)2.6 Limits at InfinitySpecial Limit: lim as x->inf 1/x = 02.6 Horizontal AsymptotesReview of Polynomial Division & Oblique Asymptotes2.2 Vertical AsymptotesWeek 3 (Unit 1: Limits)Review of Exponentials and LogarithmsPiece-wise FunctionsReview of Domain and Range2.5 Continuity2.5 Combinations of Continuous Functions pg. 1172.5 Library of Continuous Functions pg. 120 Theorem 72.5 Limits of Composite Functions2.5 Intermediate Value Theorem pg. 122Week 4 (Unit 2: Derivatives)Public Exam #5,9,212.7 Derivatives by Definition2.8 Equations of Tangent LinesSpecial Cases where Derivatives fail to exist (pg. 158)Exam 1 MONDAY February 3, 2020 (Practice Exam)Week 5 (Unit 2: Derivatives)3.1 Derivative RulesSpecial Derivative: The derivative of e^x = e^x3.2 The Product Rule3.2 The Quotient RuleWeek 6 (Unit 2: Derivatives)3.7 (Revisit 2.7 and 2.8) to discuss position-velocity-acceleration3.3 Trigonometric Derivatives3.4 The Chain RuleWeek 7 (Unit 2: Derivatives)3.5 Inverse Trigonometric Derivatives3.5 Implicit DifferentiationThese lecture notes will be helpful to read PRIOR to beginning 3.6Special Derivative: The derivative of ln(x) is 1/x3.6 Derivatives of Logarithms & Logarithmic Differentiation as a techniqueEquations of Normal LinesUnit 2 Exam Monday March 2, 2019Week 8 (Unit 3: Derivatives Applications)3.9 Related Rates9.2 Review: Slope FieldsBasic Calculator Use:Week 9 (Unit 3: Derivatives Applications) EXAM 23.10 Linear Approximations4.1 Extreme Value Theorem4.1 Critical Numbers4.1 Extreme Values: Global (Absolute) vs. Local (Relative)4.1/4.3 Finding Absolute Extrema4.2 Mean Value Theorem4.4 L'Hopitals Rule & Indeterminant Forms4.3 First Derivative Test for Local ExtremaWeek 10 (Unit 3: Derivatives Applications)4.3 Second Derivative Test4.3 Concavity4.3 Inflection Points4.3 & 4.5 Curve Sketching4.7 Optimization4.9 Anti-DerivativesWeek 11 (Unit 4: Anti-Differentiation & Integrals)Unit 3 Exam March 16, 2020Integral NotationAnti-Derivative S-V-A Word Problems5.1 Upper, Lower, Left-Hand, and Right-Hand Sums (Riemann Sums)7.7 Mid-point & Trapezoidal Sums (The last sum approximation that we will learn. Ignore everything else in this chapter that is not the midpoint or trapezoidal rule)Week 12 (Unit 4: Integrals)FORMULA PACKET6.5 Average Value of a Function5.2 Integrals as Area5.1 & 5.2 Summation Notation5.2 Definite Integrals5.2 Properties of Integrable Functions pg. 385-3875.3 Fundamental Theorem of Calculus (Part II)5.4 Indefinite Integrals and Net Change Theorem Distinguish between Total (Unsigned) Area and Net (Signed) Area. (Remember, integral notation refers to signed/net area)Week 13 (Unit 4: Integrals & Unit 5 Integral Applications)5.3 Fundamental Theorem of Calculus (Part I) [And methods for adjusting limits of integration so that FTC I applies)5.5 Substitution (Also called u-substitution)9.3 Separation of Variables (Only worry about the technique for the class example in this chapter)Unit 4 Exam April 3, 2020SPRING BREAKWeek 14 (Unit 5 Integral Applications & Course Review)6.1 Area Between Curves6.2 Volumes of Solids and Cross SectionsTWO WEEK STUDY GUIDEWeek 15 (Course Review & Full Practice Exams)Week 16 (Course Review & Full Practice Exams)Week 17 (Course Review & Full Practice Exams)